David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 16 (2):182-208 (2008)
What is wrong with abstraction, Michael Potter and Peter Sullivan explain a further objection to the abstractionist programme in the foundations of mathematics which they first presented in their Hale on Caesar and which they believe our discussion in The Reason's Proper Study misunderstood. The aims of the present note are: To get the character of this objection into sharper focus; To explore further certain of the assumptions—primarily, about reference-fixing in mathematics, about certain putative limitations of abstractionist set theory, and about the effects of impredicativity in abstraction principles—which underlie it; and To advance the debate of the issues thereby raised. Thanks for helpful comments to Roy Cook and to an anonymous referee. CiteULike Connotea Del.icio.us What's this?
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Stewart Shapiro & Geoffrey Hellman (forthcoming). Frege Meets Aristotle: Points as Abstracts. Philosophia Mathematica:nkv021.
Bob Hale (2011). The Bearable Lightness of Being (Vol 20, Pg 399, 2010). Axiomathes 21 (4):597 - 597.
Jonathan Payne (2013). Abstraction Relations Need Not Be Reflexive. Thought: A Journal of Philosophy 2 (2):137-147.
Similar books and articles
Timothy Colburn & Gary Shute (2007). Abstraction in Computer Science. Minds and Machines 17 (2):169-184.
Bob Hale & Crispin Wright (2009). The Metaontology of Abstraction. In David John Chalmers, David Manley & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press
Kit Fine (2002). The Limits of Abstraction. Oxford University Press.
Matti Eklund (2009). Bad Company and Neo-Fregean Philosophy. Synthese 170 (3):393 - 414.
Rafal Urbaniak (2010). Neologicist nominalism. Studia Logica 96 (2):149-173.
Stewart Shapiro (2004). The Nature and Limits of Abstraction. [REVIEW] Philosophical Quarterly 54 (214):166 - 174.
Steven Rappaport (1996). Abstraction and Unrealistic Assumptions in Economics∗. Journal of Economic Methodology 3 (2):215-236.
Peter Sullivan (2005). What is Wrong with Abstraction? Philosophia Mathematica 13 (2):187--93.
Michael Potter & Peter Sullivan (2005). What Is Wrong with Abstraction? Philosophia Mathematica 13 (2):187-193.
Added to index2009-01-28
Total downloads74 ( #42,188 of 1,725,442 )
Recent downloads (6 months)4 ( #167,246 of 1,725,442 )
How can I increase my downloads?